

A039787


Primes p such that p1 is squarefree.


15



2, 3, 7, 11, 23, 31, 43, 47, 59, 67, 71, 79, 83, 103, 107, 131, 139, 167, 179, 191, 211, 223, 227, 239, 263, 283, 311, 331, 347, 359, 367, 383, 419, 431, 439, 443, 463, 467, 479, 499, 503, 547, 563, 571, 587, 599, 607, 619, 643, 647, 659, 683, 691, 719, 743
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OFFSET

1,1


COMMENTS

An equivalent definition: numbers n such that phi(n) is equal to the squarefree kernel of n1.
Minimal value of first differences (between odd terms) is 4. Primes p such that both p and p + 4 are terms are: 3, 7, 43, 67, 79, 103, 223, 439, 463, 499, 643, 823, ...  Zak Seidov, Apr 16 2013


LINKS

Zak Seidov, Table of n, a(n) for n = 1..1000


EXAMPLE

phi(43)=42, 42=2^1*3^1*7^1, 2*3*7=42.
p=223 is here because p1=222=2*3*37


MAPLE

isA039787 := proc(n)
if isprime(n) then
numtheory[issqrfree](n1) ;
else
false;
end if;
end proc:
for n from 2 to 100 do
if isA039787(n) then
printf("%d, ", n) ;
end if;
end do: # R. J. Mathar, Apr 17 2013


MATHEMATICA

Select[Prime[Range[132]], SquareFreeQ[#1]&](* Zak Seidov, Aug 22 2012 *)


PROG

(MAGMA) [p: p in PrimesUpTo(780)  IsSquarefree(p1)]; // Bruno Berselli, Mar 03 2011
(PARI) is(n)=isprime(n)&&issquarefree(n1) \\ Charles R Greathouse IV, Jul 02 2013


CROSSREFS

Cf. A000010, A007947, A049092 (complement).
Sequence in context: A165318 A108184 A049091 * A226937 A227199 A129940
Adjacent sequences: A039784 A039785 A039786 * A039788 A039789 A039790


KEYWORD

nonn


AUTHOR

Olivier Gérard


EXTENSIONS

More terms from Labos Elemer


STATUS

approved



